Metcalfe's law

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Metcalfe's law states that the value of a telecommunications network is proportional to the square of the number of users of the system (n²). First formulated by Robert Metcalfe in regard to Ethernet, Metcalfe's law explains many of the network effects of communication technologies and networks such as the Internet and World Wide Web.

The law has often been illustrated using the example of fax machines: A single fax machine is useless, but the value of every fax machine increases with the total number of fax machines in the network, because the total number of people with whom each user may send and receive documents increases.

1 Revisions
2 Applications of Metcalfe's law
3 See also
4 External links

[edit] Revisions

Some argue that Metcalfe's law may exaggerate that benefit. Since a user cannot connect to itself, the reasoning goes, the actual calculation is the number of diagonals and sides in an n-gon (see also the triangular numbers):

$\frac{n(n-1)}{2}$

However, that value, which simplifies to $(n 2 - n) / 2$ , is "Big O" proportional to to the square of the number of users, so this remains the same as Metcalfe's original law.

In March 2006, Andrew Odlyzko and Benjamin Tilly published a preliminary paper which concluded Metcalfe's law significantly overestimates the value of adding connections. The rule of thumb becomes: "the value of a network with n members is not n squared, but rather n times the logarithm of n." Their primary justification for this is the idea that not all potential connections in a network are equally valuable. For example, most people call their families a great deal more often than they call strangers in other countries, and so do not derive the full value n from the phone service. In the July 2006 IEEE Spectrum, Bob Briscoe, Odlyzko and Tilly state more succinctly: "Metcalfe's Law is Wrong".^{[citation needed]} Robert Metcalfe responded to the IEEE article, defending his namesake law, on a partner's blog.^{[citation needed]}^[clarify]

In contrast, Reed's law asserts that Metcalfe's law understates the value of adding connections. Not only is a member connected to the entire network as a whole, but also to many significant subsets of the whole. These subsets add value independent of either the individual or the network as a whole. Including subsets into the calculation of the value of the network increases the value faster than just including individual nodes.

A restatement of Metcalfe's law reflects the importance to social networks of saturating the network. Many networks give the user value proportional to the fraction of friends or aquaintances who have already joined. For example, a phone system is only a useful when you are calling a friend who already has a phone.

In such situations, if $1 / n$ of the population has joined the network, then the expected value to any given user is the joint probability that both he and the person he is trying to contact have both joined the network: $1 / n 2$ , significantly less than $1 / n$ for early stage networks.

[edit] Applications of Metcalfe's law

Metcalfe's Law can be applied to more than just telecommunications devices. Metcalfe's Law can be applied to almost any computer systems that exchange data. Examples of applications include:

Metcalfe's Law frequently predicts whether a single vendor or interface standard will tend to dominate a marketplace. This has implications for whether an innovative solution can enter a marketplace that requires different interfaces.

The same law can be applied to other technological systems, such as personal genome sequencing. As more human genomes are sequenced and tied to personal health information in an interconnected system, the value of the information that a personal genome can contribute to personal health grows.